The generator matrix

 1  0  1  1  1  0  1  1  2  1  1  X  1  1
 0  1  1  0 X+1  1  0 X+1  1  X X+2  X X+3 X+3
 0  0  X  0  X  0  X  0  X  X  X  0  X X+2
 0  0  0  X  X X+2  X  0  0  0  X  X  0  2
 0  0  0  0  2  0  0  0  0  2  0  2  0  2
 0  0  0  0  0  2  0  0  2  0  2  2  0  2
 0  0  0  0  0  0  2  0  0  2  2  2  2  2
 0  0  0  0  0  0  0  2  2  2  2  2  0  0

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+114x^8+16x^9+537x^10+656x^11+2296x^12+2400x^13+4316x^14+2400x^15+2357x^16+656x^17+510x^18+16x^19+96x^20+12x^22+1x^26

The gray image is a code over GF(2) with n=56, k=14 and d=16.
This code was found by Heurico 1.16 in 0.538 seconds.